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Branch-and-Bound and Approximate Solutions to the Capacitated Plant-Location Problem

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  • Graciano Sá

    (Institute of Applied Economic Research, Rio de Janeiro, Brazil)

Abstract

In the capacitated plant-location problem, a planner is given a set of projects for production expansion and a linear transportation-cost matrix, and is asked to choose the subset of projects that meets demand at several markets, at the least production-distribution cost. The projects are defined a priori by size, location, and cost function, the latter being concave. An exact branch-and-bound treatment for the problem is explained, together with an approximate routine for solving the problem. The approximate routine borrows from the “add” approach of Kuehn-Hamburger and the “drop” approach of Feldman-Lehrer-Ray. Some of its mathematical properties are described, and sufficient conditions for the optimality of the solution obtained are shown. Empirical evidence is provided suggesting that the branch-and-bound method may be useful in problems of around 25 integer variables, perhaps more, depending on how tightly row-constrained the problem at hand is. Evidence is also provided suggesting that the approximate routine is fast and produces good, frequently optimal, results.

Suggested Citation

  • Graciano Sá, 1969. "Branch-and-Bound and Approximate Solutions to the Capacitated Plant-Location Problem," Operations Research, INFORMS, vol. 17(6), pages 1005-1016, December.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:6:p:1005-1016
    DOI: 10.1287/opre.17.6.1005
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    Cited by:

    1. Minghe Sun & Zhen-Yu Chen & Zhi-Ping Fan, 2014. "A Multi-task Multi-kernel Transfer Learning Method for Customer Response Modeling in Social Media," Working Papers 0161mss, College of Business, University of Texas at San Antonio.
    2. Fathali Firoozi, 2008. "Boundary Distributions in Testing Inequality Hypotheses," Working Papers 0046, College of Business, University of Texas at San Antonio.
    3. Sridharan, R., 1995. "The capacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 87(2), pages 203-213, December.
    4. Roe, Terry L. & Shane, Mathew, 1973. "A Heuristic Fixed-Charge Quadratic Algorithm," Staff Papers 13466, University of Minnesota, Department of Applied Economics.
    5. Zhang, Anpeng & Kang, Jee Eun & Kwon, Changhyun, 2017. "Incorporating demand dynamics in multi-period capacitated fast-charging location planning for electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 5-29.
    6. Ramesh Bollapragada & Uday S. Rao & Junying Wu, 2023. "Hub location–allocation for combined fixed-wireless and wireline broadband access networks," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(1), pages 115-128, March.
    7. Sharma, R.R.K. & Berry, V., 2007. "Developing new formulations and relaxations of single stage capacitated warehouse location problem (SSCWLP): Empirical investigation for assessing relative strengths and computational effort," European Journal of Operational Research, Elsevier, vol. 177(2), pages 803-812, March.
    8. Minghe Sun, 2008. "A Tabu Search Heuristic Procedure for the Capacitated Facility Location Problem," Working Papers 0050, College of Business, University of Texas at San Antonio.

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